Estimation Issues in Single Commodity Gravity Trade Models

Recently gravity trade models are applied to disaggregated trade data. Here many
zeros are characteristic. In the presence of excess zeros usual Poisson Pseudo Maximum
Likelihood (PPML) is still consistent, the variance covariance matrix however
is invalid. Correct economic interpretation however requires also the last. So
alternative estimators are looked for. Staub & Winkelmann [2010] argue that zeroinflated
count data models (i.e. zero-inflated Poisson / Negative Binomial Pseudo
Maximum Likelihood (ZIPPML / ZINBPML)) are no alternative since under model
misspecification these estimators are inconsistent. Yet zero-inflated Poisson Quasi-
Likelihood (PQL) is a reliable alternative. It is consistent even under model misspecifications
and beyond that robust against unobserved heterogeneity. Another
alternative is a log-skew-normal Two-Part Model (G2PM) which generalizes the
standard log-normal Two-Part Model (2PM). It is insofar advantageous as it adjusts
for (negative) skewness and regression coefficients retain usual interpretations as
in log-normal models. PQL is useful for multiplicative gravity model estimation
and G2PM for log-linear gravity model estimation. Exemplarily the estimators are
applied to intra-European piglet trade to assess their empirical performance and
applicability for single commodity trade flow analysis. The empirical part favours
PQL but G2PM is a reliable alternative for other trade flow analyses. PQL and
G2PM should become standard tools for single commodity trade flow analysis.